The Harmonics of Nature

Spoiler Alert

Let’s cut to the chase.  What if there was an underlying vibration that is at the foundation of the universe and all music?  Well, I believe there is, and it’s 7.2 Hz.  Read on for a compilation of evidence of why this seems to be the case, and how to harness it for making your own personal music in harmony with all of creation.

Introduction

The internet is full of information about sound as a healing energy.  We find debates about whether the “A” note should be tuned to 440 Hz or 432 Hz; about the healing qualities of the “Solfeggio”; videos for “binaural mind entrainment”; discussions on the correspondence between color and music; explanations of “equal temperament” vs “just intonation”; theories about the vibratory qualities of the great pyramid; the vibratory foundations of DNA; the correspondence between the angles of the Platonic solids and musical frequencies – but when we try to put all this together it doesn’t seem to gel into a cohesive pattern of actual frequencies, notes and keys to play in order to be in tune with the universe.

So, the question for me is:  Is there a foundational vibration – and related musical key which would provide the most benefit – the most connection to ourselves and each other, to the natural World around us and the cosmos we live in?

I spent about five years thinking that one key or another was “the magic key” – tuning d to different fundamental frequencies, playing out live – judging audience reaction, recording bird-song and crickets and trying to play along on the guitar, waking with songs in my head and humming them into my iPhone. Then, luck rescued me from a lifetime’s quest one night in early 2016 in a hotel room in Johannesburg.

I had thought during dinner of playing some ultra low frequencies on a tone-generator app I had on my iPhone through the new Bluetooth headphones my sister had given me for Christmas – just out of a perverse desire to hear something weird and fundamental.  As I was dialing through these low frequencies, I noticed something strange – as I turned the dial to make the tone lower, there was another whooshing-thumping sound that was speeding up – until I reached a point at 10.8 Hz where the whooshing stopped – and just sort of hovered there.

Then, turning the dial further to the left – to make the frequency slower and lower still – I noticed that the whooshing once again was speeding up – and that it then slowed down again at 7.2 Hz.  “That’s curious” – thought I.

I turned the dial further to the left – again, the whooshing sped up again and then once again slowed to halt at 5.4 Hz.

I then realized that 5.4 Hz is half of 10.8 Hz – this phenomena was occurring at two octaves of the same note: an F.  And that 7.2 Hz happens to be exactly the musical “fifth” below 10.8 Hz:  a B-flat (7.2 Hz x 3/2 = 10.8 Hz).

As it turns out, these two frequencies (5.4 and 7.2 Hz) are respectively very low octaves of the notes F and B-flat – from a “just intonation” scale based on this B-flat frequency – which also happens to position A at exactly 432 Hz.

(Interestingly, this phenomena cannot be perceived for sub-octaves of A=432 Hz (e.g. 6.75 Hz) – which indicates that B-flat and F are the source from which other harmonics are generated – and not A, as western musical convention might suggest.)

Besides the coincidence of the psycho-acoustic effect of these frequencies and the fact that they harmonically coincide with the body of knowledge around A = 432 Hz, I have discovered other intersections between these vibrations and aspects of art and science.

For example, it turns out that the “Solfeggio” – the collection of Gregorian micro-tonal frequencies which have been passed down in secret – are not a series of “magical tones” that impart healing on their own, but actually “difference notes” which when played in combinations of two or more Solfeggio notes at the same time, produce “difference” notes which correspond closely to the “magic” harmonic scale based on my B-flat and F frequencies.  The secret that was passed down through the millennia seems to be a big sign-post that says, “here are the actual notes you should be playing!”  I’ve documented this exploration here.

Meanwhile, NASA has recorded the sub-audio hum generated by black holes – which turns out to be an ultra low octave of B-flat.  I have also come across anecdotes from published writers and personal friends of musical notes that seem to “hang in mid-air” (also B-flat).  It turns out that the frequencies I discovered also correspond to “divine” numbers (54, 72, 108) from ancient Hindu texts; and I’ve found personal satisfaction in discovering that some of my favorite music from childhood happens to align with the harmonic series generated by these frequencies.

These coincidences and overlaps of knowledge have given me increasing confidence that I have stumbled across some fundamental and forgotten knowledge about the vibrational fabric of our universe – and, it seems to me, what better way to participate in “the music of the spheres” than to tune your instrument to it!

So, this blog is a collection of personal experiences and information I’ve pulled together which seem to support this discovery.  Please share your own experiences on the blog, or send me an e-mail.  It would be great to collect these shared experiences together.

Here we go:

The problems with Western music

Why does some music resonate with our essential being, and some leaves us cold, dissonant, upset or even angry?

  • Rhythm?  Sure.  “it don’t mean a thing if it ain’t got that swing” !
  • Harmony? It will certainly spruce up a simple song, and give it depth. But harmony by itself can be “lipstick on a pig”

Key?  I actually believe that the musical key and harmonic alignment, is key.  That the fundamental  resonance of a piece of music is what “moves” us.  A good example of this are the various recordings of I’m In The Mood, by John Lee Hooker (look it up on Spotify or YouTube).  The recordings in the key of G minor sound kind of Country and wild.  The recordings in E or E-flat are heavy – like the most deep, dark passion – like it really is the mood for love.

A related personal experience: in 2008, I was rehearsing with my band (the Cosmic Marvels).  The singer had written a new song in the key of B-minor.  Both the drummer and I had such a strong, visceral reaction against it that we both rebelled and refused to play it.  As our drummer later related, it was as if “every fiber of my being was reacting against the song”.  Perhaps it was too harsh, but we parted company with that singer the following week.

Similarly in 2015 – and forgetting the prior experience – I was in another band, The Moonbeeems – when I asked the band if we could try one of our songs in the key of B-minor.  When we had finished the song one of our singers  was so physically upset that she stormed out.  Now, it could have been my manner or a misunderstanding, or a coincidence, but, again – it was the key of B-minor.  And, that was basically the end of that band too.

So clearly – B minor: not a great key for band harmony!

But what is the “right” key – or right keys?  For me, the challenge is to find those vibrational frequencies that really do connect our essential being, and to construct a musical vocabulary that can be called on by musicians in the same way that poets have words with specific meaning that they combine into various rhythms and rhymes to convey “truth” and beauty.

But which vibrations shall we pick?

Unfortunately, Western culture and musical theory have left us in a shambles:

  1. The A-note is the modern reference pitch – but the evidence is that in ancient times, it was not A
  2. The vibrational frequency of that A reference pitch has been altered from its standard of 432 vibrations per second (Hertz, or Hz) documented in the 19th and 16th centuries and before, to 440 Hz made a standard in 1939.
  3. Western musical instruments are tuned to “Equal Temperament” – which approximates all notes of the 12-note harmonic scale except the octave – so that even when your piano or guitar is in tune to A, it’s out of tune with its own harmonics!
  4. Modern music seems to attach no significance to Key – so key seems to be chosen based on convenience, rather than mood or intent

To summarize: we don’t know what keys to play in; we don’t know what note should be the foundation of that key; we don’t know what frequency that note should be at; and anything we play on a piano, guitar or other fixed scale instruments isn’t even in tune with itself!

Occasionally though, we will still hear a piece of music which from its first note immediately grabs us.  Whether by fluke or inspiration, the artist had recorded the song in a certain key, with a certain “out-of-tune” instrument – or with a vibrato which somehow transcends the mechanics of making music and connects with our soul.  There is this moment of immediate resonance within us – at a deep, personal level.  Our thirst for the sacred kicks in and we rush out to hear this “gem of enlightenment” over and over.

Unfortunately, with modern electronic keyboards, and electronic tuning devices based on equal temperament, musical “happy accidents” are fewer and further between.  Jimi Hendrix is no longer spending hours tuning his guitar until it feels right – or pulling the be-jesus out of his whammy bar to hit the right sounds.  The old piano at Dynamic Studios in Jamaica has been replaced by electronic keyboards that play exactly according to the broken Western conceptions of what musical notes should be.  We are locked into 440 Hz and Equal Temperament.  And now, through the “miracle” of “Auto-Tune”, our human voices – the most essentially emotive component of music – are being altered in recordings and live performances to align with the Equal Temperament keyboard instead of aligning the keyboard to the natural harmonics of the human voice – (which, by the way, is entirely possible to do with the more sophisticated modern keyboards).  Add to this, the harmonic-stealing medium of “digital” and the increasing scarcity of live music, and we’re in a pretty sorry state.

DJs? – sure, gotta love ’em.  But re-assembling music recorded in equal temperament and 440 Hz, with no real understanding of key just leaves us parked somewhere between the 1960 and 1980s – forever sampling and repeating the same sorry dance.  And meanwhile, all of this harmonic deficiency is covered up with hyper-bass until all we can do is drink ourselves into oblivion to make it sound alright.  No wonder people stay home and watch the TV – and what do they see?  A world increasingly destroyed by our own dis-harmony and lack of sympathy and insight.

Even our options are wearing thin.  Digital recordings of “primitive” music from India, or Ireland or the Amazon or Indonesia – digitally recorded and then compressed for quick streaming download, and, if recorded in a studio – probably re-calibrated to A = 440 Hz, Equal Temperament.

So, where is the music that can penetrate our daily dross and re-connect us to our cosmic vibratory dance?

Evidence of fundamental natural vibration

Well, let’s start with the cosmos then.  NASA tells us that the vibration detected from black-holes in deep space (and time) resonates at a B-flat, 57 octaves below what we can hear.

Now, if that was it, our quest might be over.  But there’s lot of incompatible and contradictory information out there – e.g. we find discussion of the resonant nature of the Pyramids in Giza (F-sharp – which isn’t part of the B-flat harmonic series, see Appendix); or discussion about the resonance of the Earth as it interacts with its atmosphere (the Schumann resonance, 6.5 Hz to 7.8 Hz – well, which is it?), or Solfeggio frequencies, etc. It’s  difficult to build a coherent picture of our fundamental musical vibrations from all this conflicting information.  One can also try the path of intuition, but at some point – but how nice would it be to just know what the notes are supposed to be, and get on and play them?!

Harmonic “still points”

Luckily, one evening in a hotel room in Johannesburg, it occurred to me to play some very low, sub-audible frequencies on a tone generator app on my iPhone – just to see what they sounded like through the Bluetooth headphones given to me by my sister for Christmas.

While wheeling through the frequencies at around 6 vibrations-per-second (6 Hz) I noticed a “beating”.  Now, 6 Hz is not a “note” – it’s basically a very fast rhythm.  Imagine a drummer hitting a drum 6 times per second.  But, what was remarkable was not the rhythm of 6 beats per second, but instead a “swooshing” or “beating” sound – like a steam-train – that repeated about once per second.

Players of stringed instrument are familiar with the “beating” sound when tuning a note on one string to match the same note played on another string:  There is a rhythmic oscillation that occurs at the “difference frequency” between the two notes:  If the two notes are 1 Hz apart, the “beating” oscillation will be once per second.  The musician will tune the string until the “beating stops” [masochism joke here] – that’s when the two notes are identical, and are in-tune.  You can hear Joe Walsh demonstrating this at 3:14 here.

But my tone-generator wasn’t generating two frequencies – it was generating one.  So, if I was hearing a “beating”, swooshing oscillation at these low frequencies, the tone-generator would have to be interacting with some other, ultra-low “background” frequency in my environment.  So, what was the other “ghost” frequency that it was beating against?

As I slowly modified the frequency towards 5.4 Hz, the beating slowed to a stop.  Interestingly, 5.4 Hz is exactly the note F – (see Calibrating the Tuner, in Appendix).

5.4 Hz

Curious, I turned the wheel away from 5.4 Hz.  And the rate of beating/swooshing increased.  Then as the frequency approached 7 Hz the rate of beating slowed again.  So, I’m speeding up the frequency of the “note” but the swooshing noise is slowing.  At 7.2 Hz, the beating again slows to a stop.  7.2 Hz is exactly a B-flat on my tuner, calibrated as described in the appendix.  And the two frequencies 5.4 (above) and 7.2 Hz (an F and a B-flat) are exactly a musical fifth interval apart (in a 3/2 ratio).

“Curiouser and curiouser”, I thought.  One note creating interference patterns with some unheard vibration is one thing.  Two, musically related frequencies having the same effect confirms the harmonic and musical nature of what I was experiencing.  These two harmonically related frequencies – 5.4 and 7.2 Hz – were vibrating against some other “background” tone, that I couldn’t hear.

7.2 Hz

Moving the dial on, the same occurred at 10.8 Hz – double the frequency of 5.4 Hz, an octave of the first F.

So, we have a sort of Pythagorean resonance occurring at three frequencies (5.4 Hz, 7.2 Hz and 10.8 Hz), a musical fifth and an octave – vibrating in consonance with some hidden, sub-audible frequency.

But, where was the second vibration coming from – the cause of the interference pattern and the “beating”?

  • From something in the room?  The fridge?  I tried it out on the balcony – same effect.  And I’ve tried it in England and the US – same thing
  • From the tone-generator itself?  I re-calibrated it to 440 Hz and equal temperament, to see if that was a factor.  Same thing
  • Was it an artifact of Bluetooth itself?  The carrier wave of Bluetooth is standardized at 2.5 GHz – which corresponds to a frequency of 4.47 Hz, not 5.4 Hz.  So that doesn’t seem to be a factor.

Or is that the B-flat frequency, (and its F/fifth counterpart), are a part of the fabric of our universe – as NASA’s recordings of black-holes indicate?  A sort of unheard, background vibration.  Basically, that’s what I reckon – overtones of the underlying fundamental vibration of our universe are creating an interference pattern with the sub-audio vibrations from my tone-generator.

Other evidence of B-flat and F as foundational resonances

Regardless, all this could be a fluke, or the artifact of some interference in the technology.  So I looked to see if these frequencies showed up elsewhere.

Spiritual Numbers

I shared my findings with my friend, Susan Alexjander – who has done importand and inspirational research in this area, including measuring the resonant infrared frequencies returned by DNA – and has created her own music based on this, (and a wonderful piece which coincidentally combines the resonance of a black hole with a pulsar).  Her response was immediate, “54, 72, 108 – these are sacred numbers!”  I had not noticed this – but indeed, 5.4 Hz, 7.2 Hz, 10.8 Hz – if you remove the decimal places – are sacred numbers mentioned in ancient Hindu texts and elsewhere in Numerology.  Another interesting coincidence.

Ancient Instruments

I then Googled ancient musical instruments that don’t change over time such as bells, horns and flutes.  I found these cast bronze bells exhumed from ancient China:

bells002

Raising the F vibration (10.8 Hz) by a few octaves (multiply by 2 a few times) to 345.6 Hz – we now have a frequency within the range of normal music.  It’s still an F – it’s just an F we can make music with.  As it turns out, these three-thousand year old Chinese bells are based on a central tone of 345 Hz – our “F”.

As were these flutes from ancient Egypt:

flutes

Along the top of the chart above, I’ve put the frequencies of a harmonic scale based on the B-flat (7.2 Hz) and F (5.4 and 10.8 Hz) frequencies I discovered.  The four rows below this are the measured frequencies from each of the four flutes.  And I’ve highlighted in red those flute frequencies that closely match the expected frequencies of a harmonic series based on our B-flat, 7.2 Hz fundamental frequency.  That’s pretty close matches, across the four flutes, for F, G, B-flat, C and G-sharp – and all notes within a harmonic scale based on B-flat.

Just the fact that the first note of the first flute is just 0.1 Hz from our 345.6 Hz “discovered” frequency for F is pretty amazing.  It suggests that this flute maker knew this frequency, strove to match it in his/her flute making, and had a pretty amazing means for checking the instrument’s alignment with this frequency – presumably not a digital tuner!

The audible difference between 345 Hz and 346 Hz for example, is barely perceptible consciously – and yet this ancient flute-maker matched that tone not by 1 vibration per second, but by 0.1 vibrations per second!  The other flute is still only 2 Hz off, at 343 Hz.

And if we raise 345.6 by another octave to 691.2 Hz, we see that this note is also very closely approximated as the “high” F, in the other two flutes.

Also, three of the flutes are extremely closely aligned to each other on the B-flat note – indicating it was considered to be very important to get this note correct – perhaps there was a reference pitch for this note which they used when making these flutes.  And we see similar close matching across flutes at the notes, G, G-sharp, C – all essential notes of the B-flat harmonic series.

  • The fact that the F note is the fundamental note on two of the four flutes indicates that the Egyptians felt F to be fundamental, not A.  And in fact, of the four flutes, only one has even a remote approximation of the note A
  • And also, in all four flutes – from different times and places in ancient Egypt – the F frequency is in close proximity to the “still point” frequency I found on my tone-generator.

Cymatics

Meanwhile, Cymatics is a fascinating study showing how matter (lycopodium powder or salt, usually) resonates to create different geometries at different frequencies of vibration of a flat surface – or dish of liquid.  It turns out, the first frequency that creates a shape in this video is 345 Hz – our F note!

090316_1952_TheHarmonic2.png

As the chart below indicates, the video shows many points where interesting, geometrical shapes form, corresponding to frequencies in the harmonic series derived from our F and B-flat “still point” frequencies.  (I do realize there’s some “drift” here as the frequencies rise – but the accuracy is still around 99%, e.g. 2041/2073.6 – and I’m not an expert on any “lag” that the vibrating substrate might have with these kinds of cymatics – or whether they guys running this experiment turned the gauge onwards a little after the frequency that generated the shapes was reached.):

Cymatic Hz

But the first two frequencies at least are almost exact matches to the harmonic frequencies based on the two frequencies I had discovered on my tone generator.  Perhaps the universal resonance of B-flat detected by NASA (and its perfect 5th harmonic, the F note) does indeed imbue our daily lives with a resonance which inter-plays with every vibration and sound we feel and hear  – and this was also known to the ancients, somehow.

The Music of the Spheres

In Jacob Bronowski’s TV series,  The Ascent of Man – episode 4, “Music of the Spheres”, Bronowski demonstrates the physics of musical harmony advanced by Pythagoras and his disciples on the Greek island of Samos; showing how a stretched, vibrating string will yield different musical harmonics of the original vibration when touched at various whole-number divisions along its length.

When I watched this, aged 17, as a guitar player I already knew the interesting effect of “playing harmonics” – just touching the little finger to the string, right above the 12th fret, without even pressing down – to yield a singing, pure tone, one octave above the note of the original string; going from a low D to a higher D, for example.

Some say Pythagoras learned this from his time in Egypt – that touching a vibrating string at whole integer divisions of its length creates still nodes – equi-distant along the length of the string – like “mini” “strings within the string” – resonating at harmonic overtones of that fundamental tone.  In other words, the building blocks of melody are all encompassed in each fundamental string.  You don’t just get the octave, you also get the musical 5th interval, the major 3rd, the 7th and the 9th harmonics, depending on where along the string’s length you touch with your finger.  Every string is a little symphony all by itself.

So, maybe there’s a “string” – like the “monochord” of yore –  from which all the harmonics of universal energy emanate.

The Harmonic Series

One Monday morning in early 1994 – being between jobs – I went to the trouble of playing harmonics at measured distances along the guitar string, and figuring out what note was generated where.

  • Touching the string at the mid-point gives us an octave because the string is now vibrating in two parts, each at twice the original rate.
  • Playing a harmonic, one third of the distance along the string creates two “still point” nodes – three equal divisions of the string – all vibrating at three times the rate of the original, to provide what is called the “fifth” in music (because it actually takes 5 notes up the scale to go from the first note to this note)
  • Touching the string a quarter of the way along its length generates another octave
  • At a 5th of the length of the string, the musical third will be generated
  • etc.

090316_1952_TheHarmonic3.png

Image Source: https://en.wikipedia.org/wiki/Harmonic

Here are all the harmonic notes  – generated by playing harmonics on a B-flat string – starting 1/2 way along the string, going to a 9th division of the string:

Harmonics table

And, in sequence:

Harmonics table - sequence

The harmonics described above are all “over-tones” – vibrating faster than the original note.  As players of stringed instrument know, the easiest harmonics to play are:

  1. Octaves (at a point half-way, or a quarter way, down the length of the string)
  2. Fifths (at a point a third of the way down the string)
  3. Thirds (a fifth of the way along the string).
  4. “Seventh” harmonics (played at one 7th the string length) are more difficult to play – and after that it becomes difficult to get the harmonic to ring at all. They’re just not so prevalent in the fundamental note.  (Unless you’re Eddie Van Halen with a Marshall stack playing micro-harmonics).

Modern “fast Fourier” spectral analysis of sound bears this out – that the more esoteric harmonics are fainter and less resonant.  Here’s a diagram of the relative amplitude of harmonics generated by a violin:

  • Four Octaves of the fundamental note (G)
  • Two Fifths (D)
  • One Major 3rd (B) harmonic
  • One 7th (F)
  • And some un-marked notes which appear to be another Major 3rd (B), another fifth (D), another Octave (G) and an 11th harmonic (C-sharp), plus some micro-tonics

… all resonating from within the one string being played – the G.  And the relative loudness of these harmonics is in fact what differentiates the sound of a saxophone, for example, from a trumpet or a violin:Violin overtones

[Image source: University of New South Wales Physics Department]

The Rolling Stones!

What’s this bunch of reprobates doing in our voyage to the center of music?

It turns out that the 5-string “open-G” tuning taught to Stones guitarist Keith Richards by Ry Cooder in 1968 exactly follows the harmonic series.  In bold are the harmonics to which open 5-string guitar is tuned:

  1. Octave
  2. Octave
  3. Fifth
  4. Octave
  5. Major Third
  6. Fifth
  7. Seventh
  8. Octave
  9. Ninth

It’s as though the five strings are tuned intentionally to ring out the natural harmonics that are present within the first string.  5 strings resonating as one:

  1. G (fundamental)
  2. D (fifth)
  3. G (octave)
  4. B (major third)
  5. D (octave of fifth)

With the use of a capo placed across any fret you like, the fundamental note and the resonance of the entire instrument can be changed easily – to suit the inspiration of the song, while retaining the harmonic relationship between the strings – and then fretting and playing specific notes allows the inherent harmony of the vibration to be explored as rhythm and melody.

Brown Sugar, Tumbling Dice, Start Me Up – many of the hits from 1968 to the present day were written and recorded in this tuning.

Prior to that, Keith had also used 6-string open-D, open-E and open-E-flat tunings – used on such late-60s songs as Street Fighting Man, Jumpin’ Jack Flash and You Can’t Always Get What You Want – and also used by Elmore James and some of the blues and slide-guitar greats.

Keith Richards himself remarked in notes at the Exhibitionism exhibit that he is fascinated with “how one string makes another vibrate” – called sympathetic vibration.

This very insight opened up a realm of possibilities for me – in terms of playing chords while playing notes that are harmonically aligned to the fundamental resonance of the open notes.  This is the fundamental nature of music.  And, if we could find the right chords,  perhaps, this could be the fundamental music of nature!   

Keith himself has remarked that open-tuning is like a sitar – with a sort of drone note ringing in the background.  The enduring popularity of the Rolling Stones’ music, when Keith (and Mick!) have constructed songs around this approach, shows that these open tunings and the way of playing them, really “strikes a chord” with many people.

The “modes”

You get a different emotional feeling in a piece of music depending on which note of the scale it starts on – which, by the way, is usually the one it ends on – that’s how you know you’re back to the song’s point of rest – its “point of view”.

And the reason that certain music sounds happy or sad has to do with which note of the harmonic series that starting note is.  Depending on whether you start your piece of music on the first harmonic, the second harmonic, the fifth harmonic, etc – you get a very different feeling in the music.

If you have a piano handy, try playing only the white notes:

  • Starting at a C – you get a nice, jolly, major scale – found in many Christmas carols
  • Now, play the same white notes starting at an A – gives you a maudlin minor scale

Same notes – different starting note – different feeling.

This is not just because certain notes carry an emotional weight (although I believe they do) – but because the intervals – the gaps between the notes as you climb the scale from your starting note – are spaced differently depending on the starting point.

If you start a melody on the second note of the harmonic series (the A-note, if you’re still playing white notes on the piano), it forces the third note in the scale to be just a semitone above the second note – and that’s where the sound we recognize as sad comes from.  It seems to be a common, psycho-acoustic reaction across all cultures.  A scale that starts with the second note of the harmonic series is known as a “Minor” scale (or Aeolian mode).

If you start with the fourth harmonic (the C in our white-note example, above), you get a more optimistic, “major” mode.  The interval between the second and third note is a whole tone, instead of a semi-tone.  And the interval between the 7th and octave is a semi-tone – it too has a wider step.  It sounds happy, complete, robust, confident, healthy – if a little proud.  This is the “Major” (or Ionian) mode.

There is a mode name for each of the seven starting positions in the harmonic series.  For example:

  • If you start with the first note of the harmonic series, it’s called Mixolydian mode.   It sounds happy (major third), though a little poignant (minor 7th).  But, being as this mixolydian “mode” is actually the natural harmonic series itself, the music played in this mode matches the “personality” of the universe itself, in my view: “happy” yet “poignant”
  • Aeolian mode, (the familiar western “Minor” key – just doesn’t have the energy for a full major third, it also has a minor seventh.  It has humility (minor 7th) but generally lacks “get-up-and-go”.  After a while, it’s quite exhausting, like a friend who comes over and moans about their life for a few hours.  It’s a relief when it’s over
  • Major (Ionian mode) sounds pompous and over-blown after a while.  One needs a little humility (a minor 7th, perhaps) as the antidote.
  • Phrygian mode starts at the 6th note of the harmonic series – it is the basis for Flamenco – full of fire and passion, but ultimately, tragic.  It has a minor third, a minor sixth, a minor 7th.  Everything is “minored out”.

But Western “classical” music, for whatever reason, only talks about Major (Ionian) and Minor (Aeolian).  You don’t see a piece by Beethoven in G-Phrygian – even though it may be – it will likely be called “G-minor”.  And you’re more likely to see a piece in Ab-Major than you are in Ab-Lydian – even though that may really be what’s going on.  Our culture tends to simplify and obfuscate.

Mixolydian mode is generally found in folk and country music.  Because it is the only mode that reflects the natural harmonic series by including a major-third and a minor, “dominant” 7th – Mixolydian mode is the “natural” mode which describes the harmonics emanating from its fundamental note – so it is the mode we will be looking to to reflect the harmonics of our fundamental, universal tone.

Western music goes off track

This is the point at which western musical theory tends to get complicated – unnecessarily so, in my view.

The harmonic series (first, second, major-third, 5th, flattened 7th, octave) excludes two necessary intervals for western (diatonic) music: the fourth, and the sixth.  They cannot typically be found by playing a harmonic somewhere along the length of a string.

  • The fourth harmonic of the western diatonic scale, is really an “under-tone”.  It is the note below our fundamental note whose “fifth” harmonic made our fundamental note.  It’s as though there’s a string, three times longer than ours, whose fifth harmonic (played 1/3 along its length) yields our fundamental tone.  But, if there is truly a universal “drone” frequency that underlies all, then at some point there is no lower harmonic – we would be playing that fundamental vibration, itself – which the evidence presented here suggests is some octave of a B-flat.
  • The sixth note of the western diatonic scale (e.g. G in a B-flat scale), occurs harmonically as the 9th of the 5th (i.e. F is a fifth of our B-flat fundamental frequency – and G is a ninth harmonic of F).

It’s only when we derive the harmonic series for F that we get all the notes we need for the B-flat diatonic scale.  It’s as though B-flat and F resonate like a DNA spiral – only together giving us the complete tool-kit. (remember – it was B-flat and F – an exact musical fifth apart –  that I detected as “still point” frequencies on my tone-generator)

Most music theory calculates the sixth harmonic, as:

  • The 5th of the 5th of the 5th of the fundamental. For example, G is the fifth harmonic of C, which is a fifth of F, which is a fifth of our B-flat starting-point.
    • (e.g. 460.8 for a B-flat) x 3 x 3 x 3 = 388.8 Hz (when you bring the octave back down)
  • Or the sixth can be determined as the 3rd harmonic of the 4th harmonic. e.g. D-sharp/E-flat is the 4th of B-flat, and G is the 3rd harmonic of D-sharp
    • e.g. (460.8 / 3) x 5= 384 Hz

Note that these two approaches yield two different frequencies for G – i.e. 388.8 Hz and 384 Hz.  Interestingly, as you’ll see in the section on “constructing a naturally harmonic musical foundation”, my tuner says G should be 384 Hz, and my harmonic construction says it should be 388.8 Hz, based on the 9th harmonic of F .  So, there are inherent micro-tones in music which western music ignores – we are supposed to pick one.

The good news is that there are guitar builders, like Jon Catler, who recognize this and let us have both.  However, for simplicity, I’m choosing the one most closely resonant to B-flat and F, which is 388.8 Hz, as my G frequency.

The “cycle of fifths”

I was fortunate to have had a digital, sub-audio tone generator, but in the 2,5000 years since Pythagoras left us the ancient knowledge on which bells and flutes were constructed has been lost.  So, we can’t blame our forbears for making mistakes – one of which, in my opinion, being the the idea that music should be playable in any key.  It’s like saying, we’ve forgotten the ingredients for making meringues, so just whisk anything up and pop it in the oven.  Bon apetit!

Most music theorists have  held the position that Pythagoras constructed the musical scale by calculating fifths of fifths of fifths etc. until he’d derived all 12 notes of the diatonic scale.  But to me, considering how easy it is to play the 2nd, 3rd, 5th and 7th harmonics on a single string – and how faint the “harmonic of a harmonic” is to hear – I don’t see why he would veer off into a theoretical approach when he had the mechanics for generating all 7 notes of the musical scale at this fingertips – literally – by touching his finger at various geometrical points along the length of a two strings tuned a harmonic fifth apart.

Nonetheless, Western music has adopted the fifths-based approach, rather than the practical approach – and thereby unearthing a practical problem for itself, called the Lemma, or wolf-tone.

Lemma tell you a story

If you start with a basic frequency and multiply it by 3/2 you generate a musical fifth (e.g. B-flat to F) and if you repeat that multiplication by 3/2, 11 times you will make a complete round of the “cycle Of fifths” and yield all 12 notes of the western chromatic scale (as illustrated below).  But the note you end up with is not exactly the note you started with.

090316_1952_TheHarmonic5.png

For example, let’s start the cycle with a B-flat frequency of 460.8 Hz.  460.8 x 3/2 (a fifth harmonic – our F of 691.2 Hz).  And from there, if we multiply this by 11, it should take us step-by-step around the cycle-of-fifths 11 more times to bring us back to a B-flat. But what frequency do we actually end up with?

691.2 Hz x 11 = 7,603.2 Hz.  Divide that by 16 to bring it down 4 octaves and it’s 475.2 Hz – not the 460.8 Hz we started with.  And that little gap – the “lemma” – isn’t a whole note, it’s just a little chunk of dissonance – or so they thought.

So, harpsichord, piano and organ makers, tuners and composers, including Bach and Mozart, tried to account for the lemma by various schemes of “temperament” in which that gap was apportioned across the 12 intervals of the western diatonic scale – in such a way that the popular keys would suffer the least from the averaging, and the less played keys would suffer the most.  Some of these “temperaments” are pleasant, ensuring perfectly resonant 3rd harmonics in one or two keys – and certain pieces of music were written specifically for these temperaments.  In fact, Bach’s “Well Tempered Clavinet” was a series of explorations of multiple different temperaments.

Eventually, an equal apportioning of the lemma across all the intervals – known as “Equal Temperament” – was accepted as the standard way of tuning fixed pitch instruments (such as piano, organ and guitar) – because it enabled the same piece of music to be played in all keys, with equal harmonic dissonance.  It’s typical of how humanity will force the evidence to fit a theory that rather than look at what the evidence may be telling us is wrong with our theory.  So, they tried to bury the lemma and keep their view of the universe as a simple clockwork mechanism – and wait for a more enlightened age (us) to figure it out.

The averaging that Equal Temperament (ET) introduces breaks the sympathetic vibration across the harmonic series.  The whole self supporting interplay of harmonics is broken.  The music “cancels out” its own harmonics and is essentially dissonant.  Today we have food-like substances in our supermarkets – and we have music-like vibrations available for download – thanks to Equal Temperament.  Welcome to modern times!

But the universe isn’t a watch-works as our 17th century predecessors thought; its more like a harmonic web of vibrating energy.  Quantum mechanics tells us that matter is really an energy wave – photons, electrons, protons and neutrons all spinning and vibrating in harmony with each other.  Imagine if the vibration of these waves “didn’t quite add up” like the cycle of fifths doesn’t.

The lemma is fractal!

You know what else doesn’t quite add up?  Fractals: the tiniest gap at the end of the fractal ends up being a holographic mirror of your starting point.  Some scientists and authors are investigating the fractal nature of reality.

And here’s a little fractal insight I discovered for myself.  Let’s revisit that example above.  We start with our “still point” frequency of 7.2 Hz.  But that’s too low so we octave it up to 460.8 Hz to give us a B-flat we can hear – and we start the cycle-of-fifths with that frequency.   As above, 460.8 x 3/2 gives us a fifth harmonic (an F of 691.2 Hz).   If we multiply that by 11, it should take us around the cycle of fifths 11 more times to bring us back to B-flat. What frequency do we actually get (once we octave it down a bit)? 475.2 Hz.

So, what’s the size of the Lemma? 475.2 Hz minus 460.8 Hz = 14.4 Hz.  Do you recall that our “still point” vibration for B-flat is 7.2 Hz that’s half of 14.4 Hz – an octave below.

So:

  1. We start the cycle-of-fifths with a B-flat
  2. We multiply that frequency by 3/2 to give us the musical “fifth” interval (an F)
  3. We repeat this 11 times to go all around the cycle of fifths and end up back at a B-flat
  4. And the gap that we encounter between our ending note and our starting note is a small number of vibrations per second which, it turns out, happens to be a sub-octave of the very B-flat note we began with!

So, there is no gap – just a fractal fragment which itself is a microcosm of the note we started with.  And in turn, that little harmonic fragment will generate its own harmonics – which will produce its own fractal fragment, and so on, and so on…

For some reason, music theorists didn’t examine the size of the gap at the last note of the cycle with an eye to it being a harmonic of the first note.  Instead, they felt this was a fundamental flaw in nature – in the “music of the spheres” – and attempted to make it disappear.

So, the Lemma is not some useless, unexplainable gap.  The Lemma is another harmonic of our starting frequency.  And thus the cycle of fifths does not negate harmony.  It reinforces it and perpetuates it – just as a fractal perpetuates itself in the tiniest left over detail which contains the seed of the whole.

Did no-one else notice this before they went off any invented all the different “temperaments” of western music to try and eliminate this gap – including the abomination that is Equal Temperament?  Beats me – the idea came to me at 2 o’clock in the morning in 2017, and it’s pretty simple mathematics to prove it out.

For a more detailed exploration of this, take a look at my “lemma” page, here.

Foundations

OK – so musical harmony is fractal – the cycle-of-fifths is like a universal, harmonic fractal generation engine.  But if matter is vibration – all held in delicate interplay – is their a cosmic “first energy” which sets it all in motion?  The starting frequency for the cycle-of-fifths, as it were?

The good news is, I believe, is that we know what it is – it’s the 7.2 Hz “still point” vibration I stumbled across it with my tone-generator.  It is a B-flat vibration which intersects our sub-audio plane like a ripple of energy, reinforcing vibrations which align to its harmonics and cancelling out those that are en-harmonic.  A wave of natural harmony for us to align ourselves to.

Constructing a naturally harmonic musical foundation

OK,  let’s build a musical scale the right way, from the two fundamental frequencies we discovered for B-flat and F.

(If you get lost here, you can scroll down to the big chart where I summarize all the notes that I find in the small tables, below.)

The first table below investigates the harmonics based on the “still point” vibration of 7.2 Hz (B-flat) that I had discovered on my tone generator.

B-flat

  1. Starting with a frequency of 230.4 Hz (several octaves above 7.2 Hz), we treat this frequency of 230.4 Hz as though it is the frequency of a vibrating string, and then divide that string successively by 3, 5, 7, 9 (see the “Multiplier” column) to calculate the harmonic frequencies that we would get by touching the string at these “nodal” points.
  2. The second column is the name of the musical interval generated at each of these points – e.g. with the Multiplier of 3 (touching the string at a point 1/3 along it’s length) we generate the musical interval which is called (in a typically confusing manner) “the fifth” – because it is the 5th note when you play do-re-mi.
  3. The third column is the name of the note that these harmonics correspond to.  Because we started with a B-flat, the “fifth” is an F, the “third” is a D, and so-on
  4. The 4th column is the actual frequency which results
  5. In the “5ths-based Frequency” column, I put what my calibrated tuner says is correct for that named note, calibrated as it is, for “Pythagorean Just” intonation – using the interpretation that Pythagoras used the cycle of fifths, as discussed above.  Those items in red, highlight mis-matches between the harmonic frequencies we generate (column-4) and the frequencies that western theory says are supposed to occur for the starting frequency in question – because they’re in “lemma denial” 🙂
  6. Just for “shits and giggles”, I’ve added a “Gematria” column. Gematria, is the concept that by adding the integers of a number, we unearth its common, symbolic significance and harmonic value.  e.g., for the 7.2 Hz number we had found for B-flat: 7+2 = 9.  What is interesting is that EVERY “Harmonic Frequency” we generated in this chart resolves to a 9.  Another point of correlation of these “still-point” frequencies to bodies of knowledge passed down to us through the ages.

OK, so now we understand the structure of the table – let’s look at the data.  Here’s the table again so you don’t have to scroll too much:

B-flat
Table 1 – harmonics of B-flat

In the second data row (for “Fifths”) we have touched our imaginary finger one third of the way along our imaginary B-flat string.  This multiplies the frequency of the fundamental tone by 3 to give us a fifth.  (230.4 Hz  x  3) = 691.2 Hz.  And, because 691.2 number is a little unwieldy, we go down an octave and, voila, it’s: 691.2 / 2 = 345.6 Hz (F).  Yes, music lovers, we could have just multiplied the frequency by 3/2, but it’s easier for my simple brain to understand it this way – and I solved this shit, and you didn’t 🙂

  • We record this generated frequency in the “Harmonic Frequency” column. We repeat this for multipliers, 5, 7 and 9 – recording the resulting frequencies and the notes they correspond to, in the appropriate row.  The result is 4 new notes, harmonically related to the starting frequency, from which we can make chords and melody (B-flat, F, D, G#, C)

In the next table, we explore the harmonic series generated by the strongest harmonic of B-flat – its “fifth”, which is F.  You will recall that F was also the other “still point” frequency we had found.  We’ll octave it up by multiplying by 2 a few times: (10.8 Hz > 21.6 > 43.2 > 86.4 > 172.8 > 345.6 Hz = F, and make that F our starting-point in the table:

F
Table 2 – harmonics of F

Finding the harmonic series based on F (table 2) yields three new notes:  the Major Third of F (A) – which is the major seventh of B-flat; the Dominant Seventh of F (D-sharp/E-flat) – which is the fourth of B-flat; and the Ninth of F (G) – which is the sixth of B-flat.

Note:  It turns out that when you put the Seventh found here (D-sharp/E-flat) into a musical scale with a B-flat, it should be the “fourth” harmonic of B-flat, but it sounds bad.  And to bear this out, if we generate the harmonics from this flavor of E-flat, none of the resulting harmonics resonate with our original B-flat and F frequencies – as shown in table 2b.  This is a problem which smart Just Intonation luthiers like Jon Catler have taken into account, by including both versions of the 4th harmonic in their guitar necks.

E-flat
Table 2a – harmonics of Eb (as a dominant 7th of B-flat)

Another way to calculate the fourth is as though there is a string three times longer than our original B-flat string which, if we touch it a third of the way along its length gives us a B-flat.  So, instead of 3/2, it’s 2/3.  2/3 x 460.8 Hz (our B-flat) gives an E-flat/D-sharp of 307.2 Hz (compared to 302.4 Hz).  This “fourth-based” E-flat actually sounds sweeter in a musical scale with B-flat.  So, here are the harmonic frequencies generated from this E-flat.  As you can see, this E-flat does create harmonics of B-flat and F which match our original frequencies.

E-flat - alternate
Table 2b – harmonics of Eb (as B-flat x 2/3)

Put these together, and we now have all the notes necessary for several scales: B-flat Mixolydian, B-flat Ionian (major), F Dorian, F Mixolydian.  We haven’t traversed the cycle of fifths 11 times, building up lemmas  We’ve simply collected the notes of the harmonic series of the two “still point” tones that we detected (B-flat and F) and constructed scales where every harmonic is exactly – musically and mathematically – resonant with the fundamental, “magic” tones.

We now have all that we need to construct complex, modulating music – harmonically self-reinforcing and aligned with with the background, vibrational noise of our NASA’s black-hole recordings, my experience with nodal still point vibrations on my tone-generator, ancient musical instruments, cymatics and – dare way say it? – gematria.

Originally, I had felt that we should stop with just the harmonic series for B-flat and F – and the eight notes this provides us.  But I since have felt that if we keep going, until we have generated all 11 notes of the Western chromatic scale, that we are building a full palette, circling downwards towards our “sub-lunary sphere” and therefore encompassing some of the more discordant energies that make up our existence on this plane.

So, let’s do that – might as well get the whole palette.

OK, B-flat was our starting point in the first quadrant; its fifth (and strongest harmonic) – an F – was our starting point for our second quadrant; and the fifth of that F (a C) is the starting point for the third quadrant below (in yellow).  The only new note we get from the “C quadrant” is the musical 3rd – which is an E (which is a tri-tone to B-flat, “the devil’s interval”).

C
Table 3 – harmonics of C

Also note that, in gray, the frequencies for B-flat and the D we generate from a C are slightly different from those generated as harmonics from B-flat in our first quadrant.  That “fractal harmonic entropy” which manifests as the lemma is starting to make its presence known.  My solution?  I’m going to stick with the original frequencies for B-flat and D that we had in the first table.  Remember, we don’t want to play in all keys – we want to play in the keys which resonate with our “musical DNA” frequencies for B-flat and F.

Let’s move on to explore the harmonics of our next fifth, the fifth of C which is a G.  Although, as you can see below in gray, the frequencies we are starting to get no longer match the frequencies we got for these notes in the first three tables above.  Fractal entropy is making its presence known even more emphatically – and while these may be valid frequencies if you are capable of playing spacey, micro-tonal music, I’m not.  I’m going to focus on the main harmonic alignment – ‘cos I like simple.

Each new table gives us just one new note – the third harmonic – in this case, a B – is also diminished 9th of B-flat.

G
Table 4a – harmonics of G

Note: Another way to generate a G would be as the third harmonic of the alternate E-flat harmonic we explored in table 2-b, above.  In so doing, we get harmonic equivalence for the D and A frequencies we found earlier – but a contradiction for our frequencies for F and B. Again, some luthiers will support both flavors of the 6th harmonic (G in this case), such as Jon Catler’s FreeNote 24-fret Just Intonation guitar neck.

G - alternate
Table 4b – harmonics of alternate G

The next fifth is a D.  D is also closer at hand to B-flat as the third harmonic of B-flat.  This harmonic series yields one new harmonic note, again the major-third, F-sharp – which is an augmented 5th of B-flat:

D
Table 5 – harmonics of D

And the strongest harmonic of that D is its 5th, an A which gives us the starting point for table 6 – which yields just one new note (once more the major-third), a C-sharp – which is the minor-3rd of B-flat:

A
Table 6 – harmonics of A

Note:  “A”, based on its name, might be thought of as the fundamental note of the musical scale but is actually the last table in our analysis – the most tenuous harmonic when B-flat is considered as the starting note.  Perhaps by intention or irony, western labeling of the musical notes is itself a key blunder which throws most students of music down the wrong path.

Anyway, we now have all 11 notes of the western chromatic scale – those closely aligned to B-flat and F, plus the “ugly” notes: E (from harmonic series of C), B (from the harmonic series of G), F-sharp (from D), and C-sharp (from A).

Summary of frequencies harmonically aligned with B-flat and F

Put all this together, and we have the exact frequencies in Hertz for an 11-note, chromatic musical scale that is harmonically aligned to our “still point” frequencies of 7.2  Hz for B-flat and 5.4 Hz for F:

Harmonic Notes summary

Regarding the discordant notes (B, F-sharp, C-sharp).  I would suggest that they should be used only “sparingly” and as grace-notes, because they are harmonically so distant, and discordant with our starting vibrations (B-flat, F, C).  We shouldn’t use them as the fundamentals of scales themselves, because their harmonic series would all be adrift from the B-flat and F fundamental frequencies.  But life isn’t always butterflies and rainbows, so, when you need a little “venom” in your music, there they are.  However, I submit that what the world needs now is music without venom – and so, generally, I avoid playing them.

Universally Harmonic Keys

So, focused on the keys that are most harmonically aligned with B-flat and F, we can construct music on any of the following keys and modes:

  • B-flat mixolydian:- is the same notes as:
C minor
Eb Major
F Dorian
G Phrygian
G# Lydian
  •  F is the 5th of Bb and its harmonic series adds an A (as the major third of an F) to the proceedings, and F mixolydian is the same notes as:
G minor
B-flat major
C Dorian
D Phrygian
Eb  Lydian
So, there’s the ability to blend an merge modes from across the two fundamental mixolydian keys of Bb and F.
It’s interesting to note that in the world of entropy, the fundamental principle that sets it all in motion – B-flat – really only exists in one of these tables. It’s the elephant in the room which you don’t really see.

Bar bands versus “serious musicality”

I would submit that, in a world where “music theory” is constructed on top of the cycle-of-fifths (with the apportioning of the resulting wolf-interval and therefore the harmonic destruction of the underlying tones); with the wrong reference note (A instead of the actual B-flat, a semitone below); and with the wrong reference frequency (440 Hz instead of 432 Hz) – it is no wonder that most musicians spend their time playing other people’s music, trying to capture the excitement they received from that piece of music originally – which probably originally escaped the clutches of harmonic death because the guitar was uniquely tuned, or there was a vibrato on the Hammond organ, or for whatever reason.  So, we can’t blame today’s musicians for that.

But, besides the general “inability to swing” amongst these “paint by numbers” bands,  there is another key limitation to their musicality, in my view:  Guitar “Concert Tuning” (E, A, D, G, B, E) lends itself to the keys of E, A and B – and so most easy-to-play guitar music is comprised of E, A and B chords.

Most guitar players don’t question why a guitar is tuned in this way, or how it came about.  It is, and therefore that’s how they learn to play it, and these are the sounds that come out of it.  But, as we’ve seen, B is discordant with our “magic” key of B-flat, and I prefer not to play it at all, E is a tri-tone to B-flat (the “devil’s interval”) – although jazz people love that stuff.  So, if there really is a subliminal B-flat resonance in the background at all times, a good portion of the notes coming from a concert tuned guitar are going to be dissonant with it.  Solution: slap a capo on your guitar on the first fret to put it into F – and every open string is now a “non-ugly” note from our collection.

Pianists have a more even playing ground.  There is no “prejudice” to the instrument – if you’re not playing all white keys or all black keys – it’s pretty much the same level of difficulty no matter what key you’re in.  So, pianists tend to choose keys more on their aesthetic effect, rather than their playability.  This may explain why much piano music is not in E, A or B, but in B-flat, E-flat, G-minor, etc. – keys in sympathy with our magic keys.

In my view this is the fundamental difference between “bar bands” and “serious musicians”.  Serious musicians have in their midst a keyboard player, who introduces more interesting and pleasant keys.  Bar-bands are mostly driven by the guitar player.  It sounds rough – better have a beer!

Chuck Berry! – I hear you cry.  But the unsung hero of those hits was Johnny Johnson – the piano player and original band leader.  And there is a prevalence of B-flat and E-flat in those songs.

Jimi Hendrix! – I hear you cry, but after the initial pyrotechnics with the guitar tuned to concert E, he tuned down to E-flat – for songs such as The Wind Cries Mary – and all of his deeper, more numinous hits.  Hendrix transcended the guitar-driven genre – taking his music to realms of consciousness that have rarely been seen, before or since.  But he had re-tuned his instrument in order to do that.

And, in his way, so did Eddie Van Halen (also in E-flat), and of course Jimmy Page – with DADGAD and other unconventional tunings.

In the Beatles, Paul McCartney tended to write songs in B-flat, F and C because, as a bass-player, he was less limited by the tuning of the instrument – one note at a time, from across the fret-board.  He once taught a friend of mine the B-flat major chord, because as he said, “all the best songs are in B-flat.”  Whereas John Lennon, as a guitarist, tended to write songs with E, A and B in them – and, somehow, we judge John’s songs as musically more limited than the songs written by Paul McCartney and George Harrison.

Another interesting thing about the Beatles is that they became quite interested in the frequency 444 Hz – and used this as their reference pitch for tuning instead of the “destructive” 440 Hz, and the 432 Hz of our tuning – (although, we know better that the reference note should be B-flat and not A, anyway.)  I’m not sure where they got that idea from, but it doesn’t fit with the harmonic series that I’m seeing- although props to John Lennon for tuning his grand piano according to 444 Hz for Imagine which is a good song – despite also being in a “wrong” key, however 🙂

Powerful songs in the “magic keys”

Music is a subjective thing.  We like what we like.  In the end, no-one cares about the science – so long as the music moves us.  So, I started a little experiment where I found some of the most iconic pieces of music that I’ve grown up with – the ones which have really moved me, or just totally seemed to rock – and examined them to see if they are in the “magic keys” that the aforementioned study brought me to.

I’ve started to build a public playlist (which you can check out on Spotify) of these songs in the Magic Keys, as I came across them.  The list is just scratching the surface, but I add to it as I get around to it.

First up, Your Song, by Elton John.  For me, it was always this incredibly poignant love song that underlined the feelings I had for a girl at school when I was 9 years old.  Lo-and-behold, all the notes of the song fall within our magic keys – without any of the “ugly” ones.

Interestingly, Getting in Tune by the Who, a song which starts with the lyric, “I’m singing this note ‘cos it fits in well with the way I’m feeling” is, in fact, in the magic key – at least until the very end when they fancy it up a bit.

One interesting exception is Jumpin’ Jack Flash, by the Rolling Stones.  For me, it’s one of the most powerful, exhilarating riffs and songs out there, but it’s in B.  Our “no-no” key because it is one semi-tone away from our starting note of B-flat, and therefore most harmonically contradictory to it.  Well, it turns out, now that the bootleg of the original recording is available, that it was originally recorded in C, using only our “magic” notes – and seems to have been slowed down in post-production to a B – perhaps to make Jagger’s voice sound more manly (insert humour here).  The way the song was recorded is interesting because it started with Keith Richards playing acoustic guitar into an early Philips cassette recorder, over-driving the internal microphone and gain stage on the recorder to achieve a form of distortion combining the crispness and harmonic depth of an acoustic guitar with the harmonic rounding that occurs when a signal is over-driven through an analog gain stage.  This acoustic guitar track was then played back through the studio monitors, or headphones, and Charlie Watts added the drum track on top of the guitar track – which of course is backwards to how it is usually done.  So, the evidence is that the song was recorded once in C, and therefore encapsulates with it all the universal harmonic content that goes with the “magic keys” – and that this entire encapsulation was then slowed down to a B in post-production, for release.  It retains its original harmonic resonance, but it’s given to us as a sort of slowed-down, microscopic examination of that harmony.  Very trippy.

It’s a Long Way to the Top by AC/DC is in the key of B-flat, but includes C#, which I personally regard as being outside the magic keys.  But there is a power there because it drones, (with the bagpipes, no less!) on that B-flat note.  I will add, based on my section on Synesthesia, where I characterize C-sharp as being “over-reaching”, for a song that is about musical ambition, this C-sharp seems to be exactly the right note for that sentiment.  I’ve always loved the bagpipes, and B-flat is the note that the instrument naturally drones in.  It’s always fun when aesthetics meets science and they agree.

If you’re a Kyuss fan, you’ll be pleased to know that almost their entire catalog is played in C-Dorian mode – within our magic keys.  Something about playing out in the desert with a generator and only the peyote and the stars to inspire you, perhaps.

Truth hiding in plain sight

So, there we were, trawling the depths of ancient history for flutes and bells that might be tuned to our “magic keys” of B-flat mixolydian and F mixolydian – and it turns out that just about every modern horn or brass instrument is built with these keys as its fundamental resonance:

  • Most modern flutes are in B-flat – plus C and G.  All keys aligned with B-flat and F.
  • A quick check on Wikipedia reveals that the modern Trumpet is also in Bb.  Also, the Cornet, Baritone Horn, Flugel Horn, Euphonium.
  • Tubas and saxophones are in Bb, F, C or Eb – all three of the “magic” myxolydian keys – and Eb is mostly an extension of that.
  • French horns are F or Bb.
  • The Mellophone (whatever that is) is in F.

(Although the point at which these horns intersect with the A note is designed to be A=440 Hz in modern instruments.  You can counter this by pulling the mouth-piece out a little so that A=432Hz, and B-flat=460.8 Hz).

Conclusions

So, my thought process was this:

Through luck, I discovered two “fundamental” notes that seem to be “the still point of the turning universe” – to paraphrase T.S. Eliot.  That’s two vibrations at the sub-audio level of 5.4 and 7.2 Hz which seem to be in unison with some unknown, hidden frequency that creates a “beating” interference pattern with frequencies on either side of these vibrations.

So, we assume that these fundamental vibrations emanate sympathetic vibrations according to the natural, harmonic series.

Based on two iterations of the cycle of fifths, we essentially have our two original “still point” frequencies and the harmonics they generate.

So, like strands of DNA, spiraling harmonically through time and space, we have two basic tones (7.2 Hz and 5.4 Hz), creating harmonic content as they go – and providing us a rich palette to draw from for any style of music – from jazz to modal folk music – while staying in harmony with the experienced universal resonance of the B-flat and F tones.  This, to me, is a good foundation on which to build musical compositions!

Reinforcing my personal experience of 5.4, 7.2 and 10.8 Hz being foundational, resonant still points, we have found:

  • NASA’s detection of a B-flat resonance across the universe
  • Appearance of the numbers 54, 108 and 72 as ancient sacred numbers
  • Ancient musical instruments (bells and flutes) constructed around these frequencies
  • That calibrating my tuner so that B-flat = 460.8 also makes A = 432, which is considered by many to be the correct frequency for A (as opposed to 440 Hz, the current “impostor”!)
  • That every tone in our “magic” harmonic scale has a Numerologic value of 9 (considered the sacred number of completion and balance).
  • That this harmonic series encapsulates the frequencies of 432, 540, 360 and 144 which all feature in geometry as the sum of angles in platonic solids, or the size of the sun in relation to the moon, etc.
    • Before the discovery of this harmonic series based on B-flat = 7.2 Hz, it was not thought that there was a harmonic series that encapsulated all these frequencies
  • That, in retrospect, most of my favorite music has always been in the “magic keys”

Together, this is a combination of luck, witnessed physical phenomena, historical alignment, inspiration by others on this same quest and aesthetic enjoyment – the perfect combination – if you’re a collaborative, scientific aesthete like myself!  It shows that we should re-examine what music is, what frequencies should – and should not – be played; hopefully to restore our planet to the harmony that our vibrational thoughts and our vibrational energy should be attuned to, for a peaceful, just, loving and caring society – which honors the natural world, and seeks to do all in its power to conserve, nurture and love our planet, our co-inhabitants, and ourselves.

I hope we’ll get some feedback and contributions from others (or any kind of acknowledgement really, ya bastards) – in the ongoing human movement back to harmony.

I accept that my ability to draw traffic to this blog is limited.  So, please do us all a favor and share this with your friends – and your enemies, why not?!

Appendix

Calibrating the Tuner

I have the “CLEARTUNE” tuner App installed on my iPhone.  I like it because it is both a tuner and a tone generator, it can be calibrated so that any frequency can be set as “A” instead of the normal 440 Hz, and it can be set for “Pythagorean Just” temperament (cycle of fifths) – so that it is not trying to average the wolf-interval across the notes of the scale as with “Equal Temperament” on most tuners.  It also plays through headphones, via Bluetooth.

As you recall, I had found three frequencies that seemed to be resonant “still points” of universal vibration: 5.4, 7.2 and 10.8 Hz.

So, I calibrated my tuner to 460.8 Hz (7.2 Hz  x 2 x 2 x 2 x 2 x 2 = 460.8 Hz, which is a B-flat), as my reference “A” frequency, and then set the Transpose function to “minus 1”.  (This makes sense as A is one half-step below B-flat):

Tuner calibration2

Amazingly, when I did this, the tuner’s reading for “A” came out to be 432 Hz – which is considered another of those magical frequencies having to do with the speed of light and the ratio of the Moon to the Sun, etc.  That, by itself was further evidence that the frequencies I had found were confluent with other people’s research into fundamental frequencies – “research”, I might add, that goes back beyond Verdi and Zarlino in the 16th century.

(A = 440 Hz was a new standard master-minded by the English and the Germans, shortly before World War II, seemingly based arbitrarily on no naturally occurring vibration.  Perhaps it is no surprise that since its introduction in the early 1900’s the World has experienced the most catastrophic and chaotic period of civilization in recorded history.)

Back to the good news.  Now we have a tuner that is calibrated to use our discovered resonance of 7.2 Hz as its reference pitch, and can assess other vibrations it detects as harmonics, in relation to this frequency.

Note, even with this calibration, some notes are slightly altered by the tuner:

  • B should be 486 Hz, the tuner shows it as 485.5 Hz
  • C-sharp should be 270 Hz, the tuner shows it as 273.1 Hz
  • D-sharp should be 302.4 Hz, the tuner shows it as 307.2 Hz
  • F-sharp should be 360 Hz, the tuner shows it as 364.1 Hz
  • G should be 388.8 Hz, the tuner shows it as 384 Hz
  • G-sharp should be 201.6 Hz, the tuner shows it as 204.8 Hz

Suggested solutions:

  1. If you’re a guitar player, pick a single note as your reference pitch – e.g. B-flat = 460.8 Hz, or A=432 Hz – and play that note on every single string (e.g. 5th fret on the first string, 10th fret on the second string, etc.) and tune your instrument in that way.  Assuming that your instrument’s intonation is set up correctly, all the other notes will be in tune (or at least as much as they can be on an equal temperament instrument like a fretted guitar! )
  2. Or, re-tune all instruments all over the world so that the note formally known as B-flat will now be called A.  This is a not very practical solution, so option 1 may be your better bet 🙂
  3. Buy a programmable tuner such as the ST-300 from Sonic Research – which I own and recommend – as it allows you to enter the exact frequency you want for each note.

Pyramid Resonance

A technical walk-through of the resonance of the pyramids of Cheops in Egypt:

http://www.livesoundint.com/archives/2000/julyaug/pyramid/pyramid.php

The author mentions several resonant points:

  • “resonant points around” 2.5 Hz (F is 2.7 Hz)
  • “Around 90 Hz I observed a strong room mode” – F is at 86.4 Hz.
  • “…and sweeping at 1.1Hz/sec — some real energy was transferred.” 1 Hz is approximately a D.
  • “What really made everyone get up and run to the exit was the resonance near 30 Hz” – B-flat resonates at 28.8 Hz.
  • “It also appears that any wind pressure across the Pyramid’s internal air shafts, especially when the Pyramid was new and smooth, was like blowing across the neck of a coke bottle. This wind pressure created an infrasound harmonic vibration in the chamber at precisely 16 Hz.” – C is at 16.2 Hz.

The author also notes, “Being a musician myself, I was especially interested to discover a patterned musical signature to those resonances that formed an F-sharp chord. Ancient Egyptian texts indicate that this F-sharp was the resonant harmonic center of Planet Earth. F-sharp is (coincidentally?) the tuning reference for the sacred flutes of many Native American shamans.”  This is of interest, but contradicts the ancient Egyptian flutes referenced earlier, and the author’s own recorded measurements, F-sharp being 2.8 Hz, while F is 2.7 Hz, and E is 2.5 Hz.

It’s not clear to me whether the Pyramid was created as a beacon of historical knowledge, as Graham Hancock has shown, or as a mechanism for generating harmonics for good (or bad) purpose.  I would propose that if the Pyramid of Cheops is resonating at F#, B and C#, that it’s intent was not good – but the evidence above seems to dispel that.

Sonic Geometry

The video by Eric Rankin on “Sonic Geometry” is very compelling and correlates the same frequencies we have found for F-sharp (360 Hz) and C-sharp (270 Hz) and A (432 Hz) to natural phenomena including the platonic solids, the diameters of sun and moon and the “great year”:
  • 2-dimensional shapes whose inner angles in degrees add up to multiples of 180 (F#, in Hz):
    • Triangle (180)
    • Square (360)
    • Circle (360)
    • Hexagon (720)
  • 2-dimensional shapes whose inner angles in degrees add up to multiples of 540 (C#, in Hz):
    • Pentagon (540)
    • Octagon (1080)
    • Flower of life (6 circles) = 2160
  • 3-dimensional forms whose inner angles in degrees add up to multiples of 360 (F#, in Hz)
    • Tetrahedron (720)
    • Octahedron (1920)
  • 3-dimensional forms whose inner angles in degrees add up to multiples of 540 (C#, in Hz)
    • Cube (2160)
  • Phenomena relating to multiples of (or numerological similarity to) 144 (D) and 432 (A):
    • 12 x 12 = 144 Hz = D
    • 2160 (C#) :
      • 2,160 = diameter of the Moon (in miles)
      • 2,160 x 12 = 25,290 = The “great year” (how many Earth years it takes for the precession of the equinoxes to complete one cycle, through all 12 signs of the zodiac)
      • 25,920 / 60 = 432 (A)
    • 432 (A) x 2 = 864 x 1,000 = 864,000
      • 864,000 diameter of the Sun, in miles
      • 864,000 number of seconds in a day

What is interesting about this video is that at 12 minutes, 50 seconds – the narrator states that “the tuning method required to reveal geometric shapes is based on a mathematical grid, rather than mathematical ratios.”  In other words – that author has not found a musical harmonic series which contains the numbers 540, 360, 144 and 432.  OK, but we have!  And our harmonic series also retains the numerological alignment to the number 9 described in the video.

So, this is an example of where simply by labeling the frequency 432 Hz with the note “A”, people assume that the A-note should be the foundation of musical harmonics.  But it is not.  See the section on my site which compares the harmonic series derived from A=432 Hz to the harmonic series derived from B-flat=460.8 Hz, as an insight.  As we have discovered above, the correct harmonic starting point is B-flat = 460.8 Hz (and, if you’re just tuning in, 4 + 6 + 8 = 18 = 9).

If you use a frequency of 460.8 Hz, as a B-flat – an octave of 7.2 Hz which I discovered as creating a “still point” of zero beats in relation to the non-audible interference frequencies around it – you have a basis which is in alignment with all the amazing things identified in the video – plus it’s actually musical – you can actually play perfectly harmonized music based on that harmonic series.

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